set samples 2001
set terminal svg enhanced size 1250 875 fname "Times" fsize 25 background rgb 'white'
set output "butterworth bode plot.svg"
 
# Butterworth amplitude response and decibel calculation.  n is the order, which is just 1 in this image.
G(w,n) = 1 / (sqrt(1 + w**(2*n)))
dB(x) = 20 * log10(abs(x))
# Phase is for first order
P(w) = -atan(w)*180/pi
 
 
# Gridlines
set grid
 
# Set x axis to logarithmic scale
set logscale x 10
 
# No need for a key
set nokey #0.1,-25
 
# Frequency response's line plotting style
set style line 1 lt 1 lw 2
 
# Asymptote lines and slope lines are the same "arrow" style
set style line 3 lt 3 lw 1
set style arrow 3 nohead ls 3
 
# -3 dB arrow style
set style line 4 lt 4 lw 1
set style arrow 4 head filled size screen 0.02,15,45 ls 4
 
# Separator between passband and stopband line style
set style line 2 lt 2 lw 1 
set style arrow 2 nohead ls 2
 
 
 
set multiplot
 
# Magnitude response
# =============================================
set size 1,0.5
set origin 0,0.5
 
# Set range of x and y axes
set xrange [0.001:1000]
set yrange [-60:10]
 
# Create x-axis tic marks once per decade (every multiple of 10)
set xtics 10
#set ytics 10
 
# No need for two sets of numbers
set format x ""
 
# Use 10 x-axis minor divisions per major division
set mxtics 10
 
# Axis labels
set ylabel "Verstaerkung (dB)"
 
# Draw asymptote lines
set arrow 1 from 1,0 to 1000,-60 as 3
set arrow 2 from .001,0 to 1,0 as 3
 
# -3 dB arrow
set arrow 4 from 2,3 to 1,0 as 4
 
# "Kennfrequenz" label uses same coordinates as the function
set label 3 "Kennfrequenz" at 2,4 l
 
# "-3 dB" label
set arrow 5 from 0.5,-6 to 1,-3 as 4   
set label 4 "-3.01 dB" at 0.5,-7 r
 
# Draw a separator between passband and stopband and label them
set arrow 3 from 1,-60 to 1,10 as 2
 
# Label coordinates are relative to the graph window, not to the function, centered at the 1/4 and 3/4 width points
set label 1 "Passband" at graph 0.25, graph 0.1 c
set label 2 "Stopband" at graph 0.75, graph 0.1 c
 
# Draw slope lines and label
set arrow 6 from 100,-20 to 12,-20 as 3
set arrow 7 from 100,-20 to 100,-39 as 3
set label 5 "Abfall: -20 dB/Dekade" at 100,-15 c
 
plot dB(G(x,1)) ls 1  title "1st-order response"
 
 
 
 
#Phase response
# =============================================
set size 1,0.5
set origin 0,0
 
# Set range of x and y axes
set yrange [-105:15]
 
# Create y-axis tic marks every 15 degrees
set ytics 30
 
# Regular numbers
set format x "% g"
 
# Axis labels
set ylabel "Phase (Grad)"
set xlabel "Kreisfrequenz (rad/s)"
 
# Draw asymptote lines
set arrow 1 from 0.1,0 to 10,-90 as 3
set arrow 2 from 0.001,0 to 0.1,0 as 3
set arrow 10 from 10,-90 to 1000,-90 as 3
 
# -3 dB arrow
unset arrow 4 #from 2,3 to 1,0 as 4
 
# "Kennfrequenz" label uses same coordinates as the function
unset label 3 #"Cutoff frequency" at 2,4 l
 
# "-3 dB" label
unset arrow 5 #from 0.5,-6 to 1,-3 as 4   
unset label 4 #"-3.01 dB" at 0.5,-7 r
 
# Draw a separator between passband and stopband and label them
set arrow 3 from 1,-105 to 1,15 as 2
 
# Label coordinates are relative to the graph window, not to the function, centered at the 1/4 and 3/4 width points
set label 1 "Passband" at graph 0.25, graph 0.5 c
set label 2 "Stopband" at graph 0.75, graph 0.5 c
 
# Draw slope lines and label
unset arrow 6 #from 100,-20 to 12,-20 as 3
unset arrow 7 #from 100,-20 to 100,-39 as 3
unset label 5 #"Slope: -20 dB/decade" at 100,-18 c
 
plot P(x) ls 1 title "Phaseantwort"
 
 
 
unset multiplot